Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
def check (r,c):
    if min(r)<0 or min(c)<0:
        return False
    for i in range(n):
        for j in range(m):
            if r[i]+c[j]!=l[i][j]:
                return False
    return True
def fill(v,r,c):
    r[0]=v
    for j in range(m):
        c[j]=l[0][j]-v
    for i in range(1,n):
        r[i]=l[i][0]-c[0]
n,m=map(int,raw_input().split())
l=[]
for i in range(n):
    l.append([int(i) for i in raw_input().split()])
'''if n==1:
    if max(l[0])!=min(l[0]):
        print -1
    else:
        print l[0][0]
        for i in range(l[0][0]):
            print "row 1"
elif m==1:
    nl=[l[i][0] for i in range(n)]
    if max(nl)!=min(nl):
        print -1
    else:
        print nl[0]
        for i in range(nl[0]):
            print "col 1" '''
tv=min(l[0])
r=[0 for i in range(n)]
c=[0 for i in range(m)]
mr=[]
mc=[]
for i in range(tv+1):
    fill(i,r,c)
    if check(r,c) and (mr==[] or (mr!=[]and sum(r)+sum(c)<sum(mr)+sum(mc))) :
        mr=list(tuple(r))
        mc=list(tuple(c))
if mr==[]:
    print -1
else:
    print sum(mr)+sum(mc)
    for i in range(n):
        for j in range(mr[i]):
            print "row",i+1
    for i in range(m):
        for j in range(mc[i]):
            print "col",i+1